CN110826158B - Spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact - Google Patents
Spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact Download PDFInfo
- Publication number
- CN110826158B CN110826158B CN201911033380.8A CN201911033380A CN110826158B CN 110826158 B CN110826158 B CN 110826158B CN 201911033380 A CN201911033380 A CN 201911033380A CN 110826158 B CN110826158 B CN 110826158B
- Authority
- CN
- China
- Prior art keywords
- meshing
- tooth surface
- tooth
- impact
- gear
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 57
- 238000012986 modification Methods 0.000 title claims abstract description 27
- 230000004048 modification Effects 0.000 title claims abstract description 27
- 238000013461 design Methods 0.000 title claims abstract description 21
- 239000013598 vector Substances 0.000 claims abstract description 79
- 230000005540 biological transmission Effects 0.000 claims abstract description 54
- 238000005457 optimization Methods 0.000 claims abstract description 12
- 238000004458 analytical method Methods 0.000 claims abstract description 11
- 238000005516 engineering process Methods 0.000 claims abstract description 5
- 230000008569 process Effects 0.000 claims description 25
- 230000009466 transformation Effects 0.000 claims description 17
- 239000011159 matrix material Substances 0.000 claims description 12
- 238000004364 calculation method Methods 0.000 claims description 10
- 238000006243 chemical reaction Methods 0.000 claims description 7
- 238000013507 mapping Methods 0.000 claims description 7
- 238000006073 displacement reaction Methods 0.000 claims description 6
- 238000007790 scraping Methods 0.000 claims description 6
- 238000007493 shaping process Methods 0.000 claims description 6
- 230000008859 change Effects 0.000 claims description 5
- 230000002159 abnormal effect Effects 0.000 claims description 3
- 230000009471 action Effects 0.000 claims description 3
- 238000004422 calculation algorithm Methods 0.000 claims description 3
- 238000009434 installation Methods 0.000 claims description 3
- 239000002245 particle Substances 0.000 claims description 3
- 230000003068 static effect Effects 0.000 claims description 3
- 230000001131 transforming effect Effects 0.000 claims description 3
- 238000013459 approach Methods 0.000 claims description 2
- 230000005489 elastic deformation Effects 0.000 claims description 2
- 238000013178 mathematical model Methods 0.000 claims description 2
- 230000006978 adaptation Effects 0.000 abstract description 3
- 238000011160 research Methods 0.000 description 4
- 244000309464 bull Species 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 230000009467 reduction Effects 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 230000007423 decrease Effects 0.000 description 2
- 230000033001 locomotion Effects 0.000 description 2
- 238000012545 processing Methods 0.000 description 2
- 230000035945 sensitivity Effects 0.000 description 2
- 239000003638 chemical reducing agent Substances 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000005284 excitation Effects 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 230000035939 shock Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
Landscapes
- Gears, Cams (AREA)
Abstract
The invention relates to a spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact, which is used for deducing a small gear tooth surface completely conjugated with a large gear according to a meshing principle, carrying out free Ease-off curved surface design according to an interdental clearance and tooth surface normal clearance generation principle, and superposing the small gear tooth surface with a conjugate tooth surface to represent the small gear modification tooth surface. And establishing a spiral bevel gear meshing impact model considering the loaded deformation of the gear teeth, and accurately calculating the actual meshing point position and rigidity of the meshing gear teeth based on the gear tooth TCA and LTCA technologies, wherein the actual meshing point is expressed as the theoretical meshing point vector of the driven wheel, which is obtained after rotating by a small angle under a meshing coordinate system, and the theoretical meshing position is determined by the intersection point of a geometric transmission error and a bearing transmission error curve. And taking the minimum maximum meshing impact force and the minimum maximum tooth surface load as optimization targets to obtain the optimal target modified tooth surface. The invention improves the strength and reduces the meshing impact force at the same time of smaller adaptation amount, and provides a theoretical basis for subsequent spiral bevel gear dynamics analysis.
Description
Technical Field
The invention belongs to the technical field of gear transmission, and particularly relates to a spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact.
Background
Hypoid gears are widely used in vehicle final drives, and with the development of speed reducer gears in high speed, heavy duty directions, intensity and vibration noise have become bottlenecks that affect product quality. When the gears are meshed, the deformation and error of the gear teeth lead to the generation of 'basic joint error' of the contact gear pairs, so that the gear teeth deviate from a theoretical meshing line at a meshing point and a meshing point, the rotating speed is suddenly changed, and out-of-line meshing impact is caused. Out-of-line engagement shock is an important vibration and noise excitation source. At present, impact research is mainly conducted on involute cylindrical gears through an analytic method and a finite element method. The analysis method is to make the gear tooth error and deformation equivalent to the meshing line, and determine the relation between the meshing impact position and the impact parameter by the inversion mapping method, and obtain the meshing impact force by the energy conversion relation during impact. The finite element method carries out numerical simulation on the gear meshing impact process by means of finite element analysis software ANSYS/LS-DYNA, is consistent with the result obtained by the analysis method, can be used for complex gear tooth surface meshing impact calculation, has higher requirements on the precision of tooth surface nodes and grid division and assembly precision, has lower calculation efficiency, and is not suitable for engineering application. The resolution method can express the engagement impact force as a nonlinear function of impact stiffness and impact velocity, which have a great relationship with impact position. The tooth surface of the spiral bevel gear is complex, the position of an initial meshing point is difficult to determine, the calculation of the impact speed is difficult, and related researches are few at present. Gear tooth shaping is an effective way to reduce vibration and noise of a gear transmission system by removing part of materials on conjugate tooth surfaces of gears so as to reduce meshing impact, meshing stiffness fluctuation and the like. The traditional spiral bevel gear design method is concentrated on a parabolic transmission error gear surface for correcting the motion parameters of a cradle type machine tool, so that the problem of concentrated stress on the edge of the gear surface is effectively solved, but the excessive amount of the gear pair is caused, and the dynamic meshing characteristic of the gear pair cannot be fundamentally improved. In order to reasonably control the tooth surface mismatch, a novel Ease-off tooth surface topology correction technology has become a research hot spot for designing and processing the tooth surface of the spiral bevel gear. At present, the Ease-off modified tooth surface is mainly applied to contact area matching verification under a light load working condition, and the design of the free Ease-off modified tooth surface cannot be realized, so that a spiral bevel gear Ease-off modified tooth surface design method based on minimum meshing impact is required to be provided so as to more accurately analyze the dynamic performance of a transmission system.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact, which is used for effectively and quickly calculating the meshing impact force, improving the strength under smaller adaptation quantity, simultaneously better reducing the meshing impact force and providing a more reasonable and scientific theoretical basis for subsequent spiral bevel gear dynamics analysis.
The invention is realized by adopting the following technical scheme:
the design method of the spiral bevel gear tooth face Ease-off modification based on minimum meshing impact firstly regards a large gear tooth face as an imaginary gear cutter according to a meshing principle, and converts the large gear tooth face into a small gear tooth face coordinate system based on a space meshing theory and coordinate transformation to obtain a small gear tooth face bit vector and a normal vector which are completely conjugated with a large gear; secondly, according to the principle of generating the clearance between teeth and the normal clearance of the tooth surface, carrying out free Ease-off curved surface design through presetting a transmission error and a normal multi-section parabolic modified curved surface, and superposing the free Ease-off curved surface design with a conjugate tooth surface to represent a small wheel modified tooth surface; establishing a spiral bevel gear meshing impact mathematical model considering the gear tooth loading deformation, and accurately calculating the actual meshing point position of meshing gear teeth based on the gear tooth TCA and LTCA technologies, wherein the actual meshing point is expressed as the fact that the theoretical meshing point vector of a driven wheel rotates by a small angle under a meshing coordinate system, the theoretical meshing point is the position determined by the intersection point of a geometric transmission error and a bearing transmission error curve, the scraping process of meshing impact belongs to an abnormal meshing process, elastic deformation also occurs in the process, and therefore the small angle is expressed as the sum of the angle of the driven wheel rotating within the scraping time of the gear tooth surface of the driven wheel and the bearing deformation angle of the large wheel; deducing the impact speed of the meshing point according to the installation relation of the bit vector, normal vector and gear pair of the actual meshing point; according to the gear tooth bearing deformation and the load distribution coefficient obtained by LTCA, accurately obtaining the rigidity of the meshing point; the method comprises the steps of obtaining meshing impact force based on an energy conversion relation during impact, and obtaining an optimal target modified tooth surface by taking the minimum maximum meshing impact force and the minimum maximum tooth surface load as optimization targets; and analyzing the influence of the load and the input rotation speed on the engagement impact force.
The invention is further improved in that the method specifically comprises the following steps:
step 1: pinion tooth surface representation fully conjugated with a large wheel
The tooth surface of the small wheel is completely conjugated when being meshed with the tooth surface of the large wheel, and the transmission ratio is equal to the nominal transmission ratio of the gear pair, so that the large wheel is meshed by the rotation angle theta 2 And the small wheel engagement angle theta 1 Is the relation of:
θ 2 ＝z 1 /z 2 (θ 1 -θ 10 )+θ 20 (1)
in theta 10 ，θ 20 Designing the meshing rotation angles of the large wheel and the small wheel at the reference point; z 1 And z 2 The number of teeth of the small wheel and the large wheel are respectively; the large gear tooth surface is regarded as a virtual gear cutter, and is converted into a small gear tooth surface coordinate system based on space meshing theory and coordinate transformation, so that the small gear tooth surface bit vector r is completely conjugated 10 Normal vector n 10 The method comprises the following steps of:
r 10 (u,β,θ 1 ,)＝M 1p (θ 1 )M pq M qr M rs M s2 (θ 2 )r 2 (u,β) (2)
n 10 (u,β,θ 1 ,)＝L 1p (θ 1 )L qp L qr L rs L s2 (θ 2 )n 2 (u,β) (3)
middle tooth surface bit vector r 2 、n 2 Respectively a gear vector and a normal vector of the original tooth surface of the large wheel; u and beta are any point parameters on the tooth surface; m is M 1p 、M pq 、M qr 、M rs 、M s2 Is a coordinate transformation matrix, L 1p 、L pq 、L qr 、L rs 、L s2 Is a corresponding 3 x 3 sub-matrix;
step 2: small wheel normal shape-modifying curved surface expression
Modifying the contact gap of the conjugate tooth surface, wherein the superposition of the interdental gap and the tooth surface normal gap is the contact gap; modifying the pinion tooth surface by presetting transmission errors and multistage parabolic modification parameters, so as to change the initial contact gap of the conjugate tooth surface; the geometric transmission error is expressed by adopting the following 4 degree parabolic polynomial:
wherein ψ is the geometric transmission error, a 0 ～a 4 Is a curve parameter; pinion tooth face position vector r only containing preset transmission error 1 Normal vector n 1 Expression references (2-4) are determined, except that the large wheel rotation angle is expressed as:
θ 2 ＝z 1 /z 2 (θ 1 -θ 10 )+θ 20 +ψ(θ 1 ) (6)
the tooth surface normal clearance shaping curved surface is shown as delta 1 (x 1 ,y 1 )，x 1 、y 1 The axial and radial parameters are the pinion tooth surfaces; for convenience of expression, the tooth surface normal clearance, namely delta, is obtained through rotary transformation mapping by a tooth profile modification curve of the following formula (7) 1 (x 1 ,y 1 )＝f(ζ(y 1 ),θ a )，θ a For rotation transformation angle, ζ is tooth profile modification amount whose expression is:
wherein e 0 、e 1 、d 1 、d 2 Is a parabolic modification curve parameter;
step 3: expression of small-wheel Ease-off modified tooth surface
On the small-wheel tooth surface only containing transmission error, then the normal modified curved surface is superimposed to obtain the defined small-wheel analysis tooth surface whose bit vector r 1r (ii) normal vector n 1r The expression is as follows:
r 1r (u,β)＝δ 1 (u,β)n 1 (u,β)+r 1 (u,β) (8)
step 4: expression of small wheel Ease-off normal shape-modifying curved surface
The Ease-off modified curved surface reflects the degree of mismatch between the pinion tooth surface and the engaged gear tooth surface, and the value of the degree is equal to the deviation between the pinion tooth surface fully conjugated with the gear and the pinion modified tooth surface, and the expression is:
δ e (u,β)＝(r 1r (u,β)-r 10 (u,β))·n 10 (u,β) (12)
step 5: ease-off shape-modified gear TCA model
According to the distance relation between the mapping curve of the instantaneous contact line on the Ease-off topological curved surface and the rotation projection plane, the tooth surface contact point is solved, and then the contact trace and the transmission error are determined, wherein the expression of the Ease-off modified tooth surface is as follows:
in the middle ofThe rotation angle of the driving and driven wheels in the meshing process of the gear pair; after simplification, 5 equations are added, and +.>For input quantity, solve for u 1 、β 1 、u 2 、β 2 、/>Obtaining a definite solution for the unknown quantity equation set;
step 6: load bearing transmission error calculation
The normal displacement of the gear teeth in one meshing period is obtained through TCA and LTCA methods, and the normal displacement is converted into a meshing line corner, namely the driven wheel bearing transmission error is expressed as:
ψ e ＝Z(R g ×e g ·n g ) (14)
wherein: r is R g 、N g 、e g The contact point position vector and the unit normal vector of the driven wheel are respectively shown, the unit vector in the axial direction is shown as a subscript g, and the Z-direction bearing deformation is shown as a driven wheel;
step 7: determination of the position of the engaged impact
In the actual meshing process of the gear teeth, the tooth tops close to the driven wheel are contacted with the tooth roots close to the driving wheel in advance to enter the meshing process, and in the further rotating process, the tooth top contact line of the driven wheel scrapes along the tooth surfaces of the pinion teeth facing the tooth roots to reach the meshing impact end position, namely the theoretical meshing position; the theoretical meshing position is the intersection point of the geometric transmission error and the load bearing transmission error curve, the meshing impact end point is continuously changed along with the continuous increase of the load, and the load gradually approaches to the meshing conversion point when the load is reduced; the position of the driven wheel that is about to enter into engagement at this time is regarded as a small angle that it is retracted on the basis of the theoretical engagement position, which is expressed as:
z in 2 For the number of large gear teeth, therefore, in the meshing coordinate system, meshing impact point position vectors and normal vectors are expressed as:
wherein R is h Bit vectors for the contact points under the meshing coordinate system; m is M s2 For transforming the large wheel dynamic coordinate system into the meshing coordinate transformation matrix L s2 Is a corresponding 3 x 3 sub-matrix;
step 8: determination of the impact stiffness of engagement
Considering that the meshing impact time is very short, the deformation of other normal meshing tooth pairs in the process is affected by the impact tooth pairs in a negligible way, and therefore, the meshing impact rigidity is the single-tooth meshing rigidity of an impact point:
wherein: f (F) p Is normal static meshing force; l (L) s Distributing coefficients for the theoretical meshing point load; z is normal bearing deformation; k (K) s Single tooth meshing stiffness for meshing position; k (K) n The gear teeth are comprehensively engaged with the rigidity;
step 9: determination of the impact speed of engagement
The impact speed is expressed as the relative speed of the impact position point along the normal vector direction of engagement during normal engagement, and the impact speed v of the engagement point s The bit vector and normal vector of the impact point are related as follows:
wherein: v 1 、v 2 The absolute velocity vector of the contact point of the small wheel and the large wheel is the absolute velocity vector of the contact point of the small wheel and the large wheel under the meshing coordinate system; e, e 1 、e 2 Is the unit vector of the axis direction of the small and large wheel, E is the origin to E of the reference coordinate system 2 The position vector of any point of the action line is an offset vector; w (w) 1 For small wheel angular velocity value, z 1 The m' transmission error is the 1 st derivative of the number of small gear teeth;
step 10: determination of the force of engagement impact
According to the impact mechanics theory, the relationship among impact kinetic energy, normal deformation of the tooth surface and engagement impact force is expressed as:
wherein: j (J) 1 、J 2 The driving wheel and the driven wheel are rotational inertia; r's' b1 ,r′ b2 The radius of the instantaneous base circle of the driving wheel and the driven wheel;
step 11: determination of optimal Ease-off modified surfaces
Optimizing the minimum maximum load of the tooth surface and the minimum meshing impact force of one meshing period, and respectively determining an interdental contact gap parameter and a tooth surface normal contact gap parameter; the optimization is performed by a particle swarm algorithm, and the objective function is as follows:
wherein y is an optimization variable; q (Q) min 、Q max Is a variable range; w is weight coefficient G 10 、G 20 And G 1 、G 2 The maximum engaging impact force and the maximum load before and after the shaping are respectively carried out.
The invention has at least the following beneficial technical effects:
the invention carries out free Ease-off curved surface design according to the tooth space and tooth surface normal space generation principle, and is overlapped with the conjugate tooth surface of the spiral bevel gear to represent the modified tooth surface, deduces the normal vector of the modified tooth surface, and accurately expresses the modified tooth surface of the spiral bevel gear through an analysis method, so that the modified tooth surface is not separated from the theoretical tooth surface, but is more flexible, the gear pair mismatch amount is smaller, and the invention is beneficial to improving the strength and improving the dynamic meshing characteristic. Based on the TCA and LTCA technologies of the gear teeth, the actual meshing point position of the meshing gear teeth is accurately calculated, and the impact speed and rigidity of the meshing point are deduced. The maximum meshing impact force and the maximum tooth surface load are optimized, the optimal Ease-off curved surface is determined at the minimum, and the reasonable adaptation quantity of the gear pair, namely the strength is ensured and the meshing impact force of the gear teeth is reduced through the comparison with the impact force of the traditional modified tooth surface and the conjugate tooth surface; along with the increase of the load, the theoretical meshing point of the modified tooth surface always gradually moves from the position of the large wheel away from the large end and the tooth top to the direction of being in close contact with the large end and the tooth top, and the position of the meshing point is not changed after the clearance between teeth is eliminated; the reduction of the rigidity of the engagement point and the engagement impact speed of the optimal Ease-off tooth surface results in a reduction of the engagement impact force, while when the engagement impact position is no longer changed, the engagement impact force gradually increases with an increase in load, and the engagement impact force increases substantially linearly with an increase in rotational speed. The numerical calculation method provides a more scientific theoretical basis method for further high-performance tooth surface dynamics analysis.
Drawings
FIG. 1 is a generating hypoid gear mesh coordinate system of the present invention;
FIG. 2a is a fourth order transmission error curve of the present invention;
fig. 2b is a schematic view of a contact wire shaped curve of the present invention;
FIG. 2c is a schematic representation of a profile modification curve of the present invention;
FIG. 3a is a schematic illustration of the start position of the engagement impact of the present invention;
FIG. 3b is a schematic representation of the end of impact with different load engagement according to the present invention;
FIG. 3c is a schematic diagram of the engaged impact velocity of the present invention;
FIG. 4a is an Ease-off curve corresponding to a theoretical tooth surface of the present invention;
FIG. 4b is an optimal Ease-off surface of the present invention;
FIG. 5a is a schematic illustration of a theoretical tooth surface multiple load bearing drive error and theoretical meshing point of the present invention;
FIG. 5b is a schematic illustration of the present invention optimal Ease-off tooth face multiple load bearing drive error and theoretical meshing point;
FIG. 6a is a schematic representation of the contact patch of a theoretical tooth surface bull wheel and the point of impact of the bull wheel meshing;
FIG. 6b is a schematic representation of the contact patch of the large wheel and the point of impact of the large wheel meshing with the optimal Ease-off tooth surface of the present invention;
FIG. 7a is a single tooth meshing stiffness comparison of a conjugate tooth flank, a theoretical tooth flank, and an optimal Ease-off tooth flank of the present invention;
FIG. 7b is a nominal condition maximum meshing impact force comparison for a conjugate tooth face, a theoretical tooth face, and an optimal Ease-off tooth face of the present invention;
FIG. 7c is a graph of the multi-load maximum impact velocity comparison for a conjugate tooth surface, a theoretical tooth surface, and an optimal Ease-off tooth surface of the present invention;
FIG. 7d is a graph of the multi-load maximum meshing impact force comparison for the conjugate tooth surface, the theoretical tooth surface, and the optimal Ease-off tooth surface of the present invention;
FIG. 7e is a graph of the multi-speed maximum meshing impact force comparison for the conjugate tooth surface, the theoretical tooth surface, and the optimal Ease-off tooth surface of the present invention;
FIG. 8 is a flow chart of the design of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings using a hypoid gear manufactured by the HFT method as an example.
As shown in FIG. 8, the spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact provided by the invention comprises the following steps:
step 1: the pinion tooth surface fully conjugate with the bull wheel. The tooth surface of the small wheel is completely conjugated when being meshed with the tooth surface of the large wheel, and the transmission ratio is equal to the nominal transmission ratio of the gear pair, so that the large wheel is meshed by the rotation angle theta 2 And the small wheel engagement angle theta 1 Is the relation of:
θ 2 ＝z 1 /z 2 (θ 1 -θ 10 )+θ 20 (1)
in theta 10 ，θ 20 Designing the meshing rotation angles of the large wheel and the small wheel at the reference point; z 1 And z 2 The number of teeth of the small wheel and the large wheel are respectively. The meshing coordinate system of the large wheel and the small wheel is shown in figure 1, and the coordinate system S s 、S r And S is q For the reference coordinate system, S 2 Is a large wheel movement coordinate system; v is offset distance, H 1 、H 2 The distance from the conical top point of the small wheel joint to the intersection point is the distance from the conical top point of the large wheel joint to the intersection point, and Σ is the axile intersection angle; regarding the gear tooth surface of the large gear as a virtual gear cutter, converting the gear tooth surface into a gear tooth surface coordinate system S based on the space meshing theory and coordinate transformation 1 In, completely conjugated pinion tooth face bit vector r 10 Normal vector n 10 Determined by the following formula:
r 10 (u,β,θ 1 ,)＝M 1p (θ 1 )M pq M qr M rs M s2 (θ 2 )r 2 (u,β) (2)
n 10 (u,β,θ 1 ,)＝L 1p (θ 1 )L qp L qr L rs L s2 (θ 2 )n 2 (u,β) (3)
middle tooth surface bit vector r 2 、n 2 Respectively a gear vector and a normal vector of the original tooth surface of the large wheel; u and beta are any point parameters on the tooth surface; m is M 1p 、M pq 、M qr 、M rs 、M s2 Is a coordinate transformation matrix, L 1p 、L pq 、L qr 、L rs 、L s2 Is the corresponding 3 x 3 sub-matrix.
Step 2: and expressing the normal shape-modifying curved surface of the small wheel. The modification changes the contact gap of the conjugate tooth surface (superposition of the tooth space gap and the tooth surface normal gap is the contact gap). The geometric transmission error reflects the initial interdental gap size, the contact line length and the contact path of the initial interdental gap are unchanged, the tooth surface load distribution and the bearing deformation between different meshing positions are changed, and the influence on vibration is larger. The tooth surface normal clearance can change the length and the contact path of the contact line, and certain edge stress concentration is avoided; both have an effect on the sensitivity to mounting errors.
When only the interdental gap modification design is included, the fact that the meshing end and the meshing end have enough transmission errors to reduce meshing impact is needed to be considered, and the interdental gaps of the contact tooth pairs in the meshing period are not far enough apart to reduce the bearing deformation amplitude is needed to be considered, so that the parabolic transmission errors or transmission error interdental gap design curves with possibly concave transmission errors in the middle part are needed to be considered, as shown in fig. 2a, and can be expressed by the following 4 th degree parabolic polynomials:
wherein ψ is the geometric transmission error, a 0 ～a 4 Can be passed through p in FIG. 2a 0 ～p 4 Data solving of points lambda 1 、λ 2 、ε 1 ～ε 4 Parameters to be determined for interdental contact gaps; pinion tooth face position vector r only containing preset transmission error 1 Normal vector n 1 The expression can be determined with reference to (2-4), except that the large wheel rotation angle is expressed as：
θ 2 ＝z 1 /z 2 (θ 1 -θ 10 )+θ 20 +ψ(θ 1 ) (6)
The tooth surface normal clearance modification design needs to consider that the tooth root and the tooth top have certain tooth profile modification to avoid edge stress concentration, and the contact trace should also avoid edge contact of the tooth top and two tooth sides, so that the modification amount of the meshing in and out ends should have certain distortion as shown in fig. 2 b; the modified surface may be represented as delta 1 (x 1 ,y 1 )，x 1 、y 1 Is the axial and radial parameters of the pinion gear face. For convenience of expression, tooth surface normal clearance, namely delta, can be obtained through rotary transformation mapping by the tooth profile modification curve of fig. 2c 1 (x 1 ,y 1 )＝f(ζ(y 1 ),θ a )，θ a For rotation transformation angle, ζ is tooth profile modification amount whose expression is:
wherein e 0 、e 1 、d 1 、d 2 Is a parabolic modification curve parameter.
Step 3: expression of small-wheel Ease-off modified tooth flanks. The normal modified curved surface is superimposed on the small-wheel tooth surface only containing transmission error, so as to obtain the defined small-wheel analysis modified tooth surface whose bit vector r 1r (ii) normal vector n 1r The expression is as follows:
r 1r (u,β)＝δ 1 (u,β)n 1 (u,β)+r 1 (u,β) (8)
step 4: and (5) expressing a normal modified curved surface of the small wheel Ease-off. The Ease-off modified curved surface reflects the degree of mismatch between the pinion tooth surface and the engaged gear tooth surface, and the value of the degree is equal to the deviation between the pinion tooth surface fully conjugated with the gear and the pinion modified tooth surface, and the expression is:
δ e (u,β)＝(r 1r (u,β)-r 10 (u,β))·n 10 (u,β) (12)
step 5: the Ease-off trim gear TCA model. The method can solve the tooth surface contact point according to the distance relation between the mapping curve of the instantaneous contact line on the Ease-off topological curved surface and the rotation projection plane, so as to determine the contact trace and the transmission error, and is basically the same as the TCA analysis principle of the digital tooth surface. The Ease-off modified tooth surface in the invention has a definite analytical expression, and the traditional TCA method is adopted here, and the expression is:
in the middle ofIs the rotation angle of the driving and driven wheels in the meshing process of the gear pair. After simplification, 5 equations are added, and +.>For input quantity, solve for u 1 、β 1 、u 2 、β 2 、/>A deterministic solution can be obtained for the system of unknown equations.
Step 6: and carrying out calculation of transmission errors. The normal displacement of the gear teeth in one meshing period is obtained through TCA and LTCA methods, and the normal displacement is converted into a meshing line corner, namely the driven wheel bearing transmission error is expressed as:
ψ e ＝Z(R g ×e g ·n g ) (14)
wherein: r is R g 、N g 、e g The contact point position vector and the unit normal vector of the driven wheel are respectively shown, the unit vector in the axial direction is shown as a subscript "g" representing the driven wheel, and a subscript "p" representing the driving wheel; the Z-direction carries the deformation.
Step 7: determination of the position of the engaged impact. In the actual meshing process, the point A of the tooth top close to the driven wheel contacts with the point A' close to the tooth root of the driving wheel in advance to enter meshing, the contact line at the point A of the tooth top of the driven wheel reaches the point A along the direction of the tooth root of the pinion to face the tooth root of the pinion in the further rotating process, and then the point A is normally meshed along the direction of a theoretical meshing line until the point A is withdrawn, as shown in fig. 3a, wherein the point A is a meshing impact end position (theoretical meshing contact position). The theoretical meshing position is the intersection point of the geometric transmission error and the load bearing transmission error curve, as shown in fig. 3b, the meshing points are A, B under the working conditions of load 1 and load 2, when the load is greater than load 2, the meshing impact point is not changed along with the continuous increase of the load, and when the load is reduced, the meshing impact point is gradually approaching to the meshing conversion point C. The position of the driven wheel to be engaged at this time can be regarded as a small angle of withdrawal based on the theoretical engagement position, and it should be noted that the scraping process of the engagement impact belongs to the abnormal engagement process, and a great deal of time and theoretical research indicate that the scraping time accounts for 5% -20% of the engagement period, and 10% is taken here, so the angle can be expressed as shown in fig. 3 c:
z in 2 For the number of large gear teeth, therefore, in the meshing coordinate system, meshing impact point position vectors and normal vectors are expressed as:
wherein R is h For engaging with seatsThe bit vector of the lower contact point of the mark system; m is M s2 For transforming the large wheel dynamic coordinate system into the meshing coordinate transformation matrix L s2 Is the corresponding 3 x 3 sub-matrix.
Step 8: determination of the impact stiffness of the engagement. Considering that the meshing impact time is very short, the deformation of other normal meshing tooth pairs in the process is affected by the impact tooth pairs in a negligible way, and therefore, the meshing impact rigidity is the single-tooth meshing rigidity of an impact point:
wherein: f (F) p Is normal static meshing force; l (L) s Distributing coefficients for the theoretical meshing point load; z is normal bearing deformation; k (K) s Single tooth meshing stiffness for meshing position; k (K) n The gear teeth are integrated with meshing rigidity.
Step 9: determination of the engagement impact velocity. The impact speed is simply expressed as the relative speed of the impact position point along the meshing normal vector direction when normal meshing, according to which the meshing impact speed of the standard involute flank must be zero, it is obvious that the calculation method is questionable, and for a modified gear, the calculated impact speed is not zero but obviously smaller because the impact point is not conjugated. The spiral bevel gear is equivalent to an equivalent cylindrical gear of the bevel gear at a theoretical meshing point, the meshing impact speed is represented as a nonlinear function of the large wheel radius of the theoretical meshing point, the bearing deformation of the large wheel meshing initial point and the rotation speed of the driving wheel by referring to the graphic method of the cylindrical gear, but the calculated impact speed error of the spiral bevel gear is larger due to the change of the pitch circle radius of the spiral bevel gear in the tooth length direction. Impact velocity v of engagement point s The calculation is as follows:
wherein: v 1 、v 2 The absolute velocity vector of the contact point of the small wheel and the large wheel is the absolute velocity vector of the contact point of the small wheel and the large wheel under the meshing coordinate system; e, e 1 、e 2 Is the unit vector of the axis direction of the small and large wheel, E is the referenceTaking the origin of the coordinate system to e 2 A position vector (offset vector) of any point of the line of action; w (w) 1 For small wheel angular velocity value, z 1 The m' drive error is the derivative of the 1 st order for the number of pinion teeth.
Step 10: and determining the engagement impact force. According to the impact mechanics theory, the relationship among impact kinetic energy, normal deformation of the tooth surface and engagement impact force is expressed as:
wherein: j (J) 1 、J 2 The driving wheel and the driven wheel are rotational inertia; r's' b1 ,r′ b2 Is the instantaneous base circle radius of the driving wheel and the driven wheel.
Step 11: and determining an optimal Ease-off modified curved surface. The tooth contact gap parameter and the tooth surface normal contact gap parameter can be determined by optimizing the maximum load minimum of the tooth surface and the minimum of the meshing impact force of one meshing period. The optimization process is a nonlinear iteration process for solving TCA and LTCA methods by changing the initial gaps of tooth surfaces, and a plurality of local solutions exist, so that an efficient optimization method needs to be found, a particle swarm algorithm has global convergence, a nonlinear optimization problem with a plurality of local extrema can be solved, optimization is performed by the method, and an objective function is:
wherein y is an optimization variable; q (Q) min 、Q max Is a variable range; w is weight coefficient G 10 、G 20 And G 1 、G 2 The maximum engaging impact force and the maximum load before and after the shaping are respectively carried out.
To verify the meshing impact profile optimizing effect of the present invention, example calculations were performed with the hypoid gear pair geometry parameters shown in table 1 and the original theoretical tooth surface machining parameters shown in table 2. And under the working condition that the rated torque of the large wheel is 1000N.m, the table 3 is the optimal Ease-off curved surface parameter.
Table 1 hypoid gear pair geometry parameters
Table 2 hypoid gear processing parameters
TABLE 3 optimal Ease-off surface parameters
The Ease-off curved surface (see fig. 4 a) and the optimal Ease-off curved surface (see fig. 4 b) corresponding to the theoretical tooth surface are matched and consistent with the contact area respectively, the contact marks of the theoretical tooth surface (see fig. 5 a) and the optimal Ease-off tooth surface (see fig. 5 b) are all in inner diagonal contact, and a certain amplitude is arranged at the meshing conversion point, so that the sensitivity of installation errors can be reduced (see fig. 6a and 6 b). Because the spiral bevel gear is partially conjugated, the position of the meshing point cannot occur at the tooth top of the large wheel, the position of the meshing impact point changes along with the load, and the theoretical meshing point always moves gradually from the position far away from the large end and the tooth top to the direction close to the large end and the tooth top along with the increase of the load; after the clearance between teeth is eliminated, the position of the meshing point is not changed any more and is always near the top of the big end tooth.
When the load is 1000N.m, the clearance between tooth surfaces of the theoretical tooth surfaces is completely eliminated, and the meshing contact point is on the tooth top of the large wheel; the meshing contact point of the optimal Ease-off tooth surface is separated from the top of the big end tooth by a certain distance, and when the load is larger than 1800N.m, the inter-tooth gap is thoroughly eliminated, so that the load born by the optimal Ease-off tooth surface at the meshing point is minimum, and obviously, the load born by the conjugate tooth surface is more, so that the single tooth meshing stiffness is maximum (see figure 7 a); as the load increases, the load bearing deformation gradually increases, the impact speed of the meshing point of the conjugate tooth surface gradually increases, the meshing point of the conjugate tooth surface changes after the modification to cause the impact speed to change, and when the meshing impact position is not changed after the clearance between teeth is eliminated (see figure 7 b), the impact speed slowly increases along with the increase of the load; the meshing impact force of the optimal Ease-off tooth surface at rated load is minimum and falls to 6% of the conjugate tooth surface mainly due to the reduction of the meshing point rigidity and impact speed (see fig. 7 c).
Under the rated rotation speed, the position of the meshing point of the conjugate tooth surface is unchanged along with the increase of the load, and the single tooth rigidity gradually increases with the increase of the meshing impact speed to gradually increase the meshing impact force; the meshing point of the modified tooth surface changes along with the increase of the load, the single tooth rigidity and the meshing impact speed decrease, so that the meshing impact force decreases, and when the meshing impact position is not changed any more, the meshing impact force gradually increases (see fig. 7 d); at rated load, the engagement impact force increases linearly with increasing rotational speed (see fig. 7).
Claims (1)
1. The spiral bevel gear tooth face Ease-off modification design method based on minimum meshing impact is characterized in that the method firstly regards a large gear tooth face as a virtual gear cutter according to a meshing principle, and converts the large gear tooth face into a small gear tooth face coordinate system based on a space meshing theory and coordinate transformation to obtain a small gear tooth face bit vector and a normal vector which are completely conjugated with a large gear; secondly, according to the principle of generating the clearance between teeth and the normal clearance of the tooth surface, carrying out free Ease-off curved surface design through presetting a transmission error and a normal multi-section parabolic modified curved surface, and superposing the free Ease-off curved surface design with a conjugate tooth surface to represent a small wheel modified tooth surface; establishing a spiral bevel gear meshing impact mathematical model considering the gear tooth loading deformation, and accurately calculating the actual meshing point position of meshing gear teeth based on the gear tooth TCA and LTCA technologies, wherein the actual meshing point is expressed as the fact that the theoretical meshing point vector of a driven wheel rotates by a small angle under a meshing coordinate system, the theoretical meshing point is the position determined by the intersection point of a geometric transmission error and a bearing transmission error curve, the scraping process of meshing impact belongs to an abnormal meshing process, elastic deformation also occurs in the process, and therefore the small angle is expressed as the sum of the angle of the driven wheel rotating within the scraping time of the gear tooth surface of the driven wheel and the bearing deformation angle of the large wheel; deducing the impact speed of the meshing point according to the installation relation of the bit vector, normal vector and gear pair of the actual meshing point; according to the gear tooth bearing deformation and the load distribution coefficient obtained by LTCA, accurately obtaining the rigidity of the meshing point; the method comprises the steps of obtaining meshing impact force based on an energy conversion relation during impact, and obtaining an optimal target modified tooth surface by taking the minimum maximum meshing impact force and the minimum maximum tooth surface load as optimization targets; and analyzing the influence of the load and the input rotation speed on the engagement impact force;
the method specifically comprises the following steps:
step 1: pinion tooth surface representation fully conjugated with a large wheel
The tooth surface of the small wheel is completely conjugated when being meshed with the tooth surface of the large wheel, and the transmission ratio is equal to the nominal transmission ratio of the gear pair, so that the large wheel is meshed by the rotation angle theta 2 And the small wheel engagement angle theta 1 Is the relation of:
θ 2 ＝z 1 /z 2 (θ 1 -θ 10 )+θ 20 (1)
in theta 10 ，θ 20 Designing the meshing rotation angles of the large wheel and the small wheel at the reference point; z 1 And z 2 The number of teeth of the small wheel and the large wheel are respectively; the large gear tooth surface is regarded as a virtual gear cutter, and is converted into a small gear tooth surface coordinate system based on space meshing theory and coordinate transformation, so that the small gear tooth surface bit vector r is completely conjugated 10 Normal vector n 10 The method comprises the following steps of:
r 10 (u,β，θ 1 ,)＝M 1p (θ 1 )M pq M qr M rs M s2 (θ2 2 )r 2 (u,β) (2)
n 10 (u,β,θ 1 ,)＝L 1p (θ 1 )L qp L qr L rs L s2 (θ 2 )n 2 (u,β) (3)
in the middle ofTooth surface bit vector r 2 、n 2 Respectively a gear vector and a normal vector of the original tooth surface of the large wheel; u and beta are any point parameters on the tooth surface; m is M 1p 、M pq 、M qr 、M rs 、M s2 Is a coordinate transformation matrix, L 1p 、L pq 、L qr 、L rs 、L s2 Is a corresponding 3 x 3 sub-matrix;
step 2: small wheel normal shape-modifying curved surface expression
Modifying the contact gap of the conjugate tooth surface, wherein the superposition of the interdental gap and the tooth surface normal gap is the contact gap; modifying the pinion tooth surface by presetting transmission errors and multistage parabolic modification parameters, so as to change the initial contact gap of the conjugate tooth surface; the geometric transmission error is expressed by adopting the following 4 degree parabolic polynomial:
wherein ψ is the geometric transmission error, a 0 ～a 4 Is a curve parameter; pinion tooth face position vector r only containing preset transmission error 1 Normal vector n 1 Expression references (2-4) are determined, except that the large wheel rotation angle is expressed as:
θ 2 ＝z 1 /z 2 (θ 1 -θ 10 )+θ 20 +ψ(θ 1 ) (6)
the tooth surface normal clearance shaping curved surface is shown as delta 1 (x 1 ,y 1 )，x 1 、y 1 The axial and radial parameters are the pinion tooth surfaces; for convenience of expression, the tooth surface normal clearance, namely delta, is obtained through rotary transformation mapping by a tooth profile modification curve of the following formula (7) 1 (x 1 ,y 1 )＝f(ζ(y 1 ),θ a )，θ a For rotation transformation angle, ζ is tooth profile modification amount whose expression is:
wherein e 0 、e 1 、d 1 、d 2 Is a parabolic modification curve parameter;
step 3: expression of small-wheel Ease-off modified tooth surface
On the small-wheel tooth surface only containing transmission error, then the normal modified curved surface is superimposed to obtain the defined small-wheel analysis tooth surface whose bit vector r 1r (ii) normal vector n 1r The expression is as follows:
r 1r (u,β)＝δ 1 (u,β)n 1 (u,β)+r 1 (u,β) (8)
step 4: expression of small wheel Ease-off normal shape-modifying curved surface
The Ease-off modified curved surface reflects the degree of mismatch between the pinion tooth surface and the engaged gear tooth surface, and the value of the degree is equal to the deviation between the pinion tooth surface fully conjugated with the gear and the pinion modified tooth surface, and the expression is:
δ e (u,β)＝(r 1r (u,β)-r 10 (u,β))·n 10 (u,β) (12)
step 5: ease-off shape-modified gear TCA model
According to the distance relation between the mapping curve of the instantaneous contact line on the Ease-off topological curved surface and the rotation projection plane, the tooth surface contact point is solved, and then the contact trace and the transmission error are determined, wherein the expression of the Ease-off modified tooth surface is as follows:
in the middle ofThe rotation angle of the driving and driven wheels in the meshing process of the gear pair; after simplification, 5 equations are added, and +.>For input quantity, solve for u 1 、β 1 、u 2 、β 2 、/>Obtaining a definite solution for the unknown quantity equation set;
step 6: load bearing transmission error calculation
The normal displacement of the gear teeth in one meshing period is obtained through TCA and LTCA methods, and the normal displacement is converted into a meshing line corner, namely the driven wheel bearing transmission error is expressed as:
ψ e ＝Z(R g ×e g ·n g ) (14)
wherein: r is R g 、N g 、e g The contact point position vector and the unit normal vector of the driven wheel are respectively shown, the unit vector in the axial direction is shown as a subscript g, and the Z-direction bearing deformation is shown as a driven wheel;
step 7: determination of the position of the engaged impact
In the actual meshing process of the gear teeth, the tooth tops close to the driven wheel are contacted with the tooth roots close to the driving wheel in advance to enter the meshing process, and in the further rotating process, the tooth top contact line of the driven wheel scrapes along the tooth surfaces of the pinion teeth facing the tooth roots to reach the meshing impact end position, namely the theoretical meshing position; the theoretical meshing position is the intersection point of the geometric transmission error and the load bearing transmission error curve, the meshing impact end point is continuously changed along with the continuous increase of the load, and the load gradually approaches to the meshing conversion point when the load is reduced; the position of the driven wheel that is about to enter into engagement at this time is regarded as a small angle that it is retracted on the basis of the theoretical engagement position, which is expressed as:
z in 2 For the number of large gear teeth, therefore, in the meshing coordinate system, meshing impact point position vectors and normal vectors are expressed as:
wherein R is h Bit vectors for the contact points under the meshing coordinate system; m is M s2 For transforming the large wheel dynamic coordinate system into the meshing coordinate transformation matrix L s2 Is a corresponding 3 x 3 sub-matrix;
step 8: determination of the impact stiffness of engagement
Considering that the meshing impact time is very short, the deformation of other normal meshing tooth pairs in the process is affected by the impact tooth pairs in a negligible way, and therefore, the meshing impact rigidity is the single-tooth meshing rigidity of an impact point:
wherein: f (F) p Is normal static meshing force; l (L) s Distributing coefficients for the theoretical meshing point load; z is normal bearing deformation; k (K) s Single tooth meshing stiffness for meshing position; k (K) n The gear teeth are comprehensively engaged with the rigidity;
step 9: determination of the impact speed of engagement
The impact speed is expressed as the relative speed of the impact position point along the normal vector direction of engagement during normal engagement, and the impact speed v of the engagement point s The bit vector and normal vector of the impact point are related as follows:
wherein:v 1 、v 2 the absolute velocity vector of the contact point of the small wheel and the large wheel is the absolute velocity vector of the contact point of the small wheel and the large wheel under the meshing coordinate system; e, e 1 、e 2 Is the unit vector of the axis direction of the small and large wheel, E is the origin to E of the reference coordinate system 2 The position vector of any point of the action line is an offset vector; w (w) 1 For small wheel angular velocity value, z 1 The m' transmission error is the 1 st derivative of the number of small gear teeth;
step 10: determination of the force of engagement impact
According to the impact mechanics theory, the relationship among impact kinetic energy, normal deformation of the tooth surface and engagement impact force is expressed as:
wherein: j (J) 1 、J 2 The driving wheel and the driven wheel are rotational inertia; r's' b1 ,r′ b2 The radius of the instantaneous base circle of the driving wheel and the driven wheel;
step 11: determination of optimal Ease-off modified surfaces
Optimizing the minimum maximum load of the tooth surface and the minimum meshing impact force of one meshing period, and respectively determining an interdental contact gap parameter and a tooth surface normal contact gap parameter; the optimization is performed by a particle swarm algorithm, and the objective function is as follows:
wherein y is an optimization variable; q (Q) min 、Q max Is a variable range; w is weight coefficient G 10 、G 20 And G 1 、G 2 The maximum engaging impact force and the maximum load before and after the shaping are respectively carried out.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911033380.8A CN110826158B (en) | 2019-10-28 | 2019-10-28 | Spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911033380.8A CN110826158B (en) | 2019-10-28 | 2019-10-28 | Spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110826158A CN110826158A (en) | 2020-02-21 |
| CN110826158B true CN110826158B (en) | 2024-02-02 |
Family
ID=69551120
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911033380.8A Active CN110826158B (en) | 2019-10-28 | 2019-10-28 | Spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110826158B (en) |
Families Citing this family (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111666643B (en) * | 2020-06-16 | 2024-01-26 | 重庆大学 | Method for determining contact performance of complex tooth surface |
| CN112036039B (en) * | 2020-09-01 | 2022-12-23 | 内蒙古科技大学 | High-precision numerical analysis method for thermal performance of conjugated heat transfer material |
| CN113111454B (en) * | 2021-04-01 | 2024-08-23 | 浙江工业大学 | RV reducer dynamic transmission error optimization method based on Kriging model |
| CN114483914B (en) * | 2021-10-27 | 2023-05-09 | 长安大学 | Point contact tooth grinding method for diagonal shaping helical gear |
| CN114239258B (en) * | 2021-12-09 | 2023-02-17 | 中国船舶重工集团公司第七0三研究所 | Herringbone gear shape modification quantity optimization design method fluctuating according to meshing period |
| CN114756988B (en) * | 2022-04-08 | 2024-05-10 | 湖南科技大学 | Crack spiral bevel gear time-varying meshing stiffness calculation method based on correction finite element |
| CN116842664B (en) * | 2023-09-01 | 2023-11-21 | 溧阳渐开机械传动科技有限公司 | Tooth surface forward design method, device and medium for meshing performance requirements |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0953702A (en) * | 1995-06-05 | 1997-02-25 | Toyota Central Res & Dev Lab Inc | Gear design, gear and gear measurement |
| WO2015154317A1 (en) * | 2014-04-10 | 2015-10-15 | 重庆大学 | Point contact gear based on conjugate curves, meshing pair and machining tool therefor |
| CN107066678A (en) * | 2017-01-22 | 2017-08-18 | 北京工业大学 | Mesh impact model with base pitch error |
| CN107131283A (en) * | 2017-06-09 | 2017-09-05 | 江苏大学 | A kind of roller gear bidentate face correction method of meter and back of tooth contact performance |
| CN107992698A (en) * | 2017-12-13 | 2018-05-04 | 长安大学 | A kind of spiral bevel gear Tooth Contact Analysis method |
| CN109145484A (en) * | 2018-09-04 | 2019-01-04 | 中南大学 | Numerical value load Tooth Contact Analysis method based on hyperboloid shell unit model |
| CN109241683A (en) * | 2018-10-31 | 2019-01-18 | 长安大学 | A kind of free tooth surface design method of helical gear |
| CN109992877A (en) * | 2019-03-28 | 2019-07-09 | 长安大学 | A kind of method of gear pair geometrical contact analysis |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7665380B2 (en) * | 2000-02-29 | 2010-02-23 | Kabushiki Kaisha Toyota Chuo Kenkyusho | Hypoid gear design method |
-
2019
- 2019-10-28 CN CN201911033380.8A patent/CN110826158B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0953702A (en) * | 1995-06-05 | 1997-02-25 | Toyota Central Res & Dev Lab Inc | Gear design, gear and gear measurement |
| WO2015154317A1 (en) * | 2014-04-10 | 2015-10-15 | 重庆大学 | Point contact gear based on conjugate curves, meshing pair and machining tool therefor |
| CN107066678A (en) * | 2017-01-22 | 2017-08-18 | 北京工业大学 | Mesh impact model with base pitch error |
| CN107131283A (en) * | 2017-06-09 | 2017-09-05 | 江苏大学 | A kind of roller gear bidentate face correction method of meter and back of tooth contact performance |
| CN107992698A (en) * | 2017-12-13 | 2018-05-04 | 长安大学 | A kind of spiral bevel gear Tooth Contact Analysis method |
| CN109145484A (en) * | 2018-09-04 | 2019-01-04 | 中南大学 | Numerical value load Tooth Contact Analysis method based on hyperboloid shell unit model |
| CN109241683A (en) * | 2018-10-31 | 2019-01-18 | 长安大学 | A kind of free tooth surface design method of helical gear |
| CN109992877A (en) * | 2019-03-28 | 2019-07-09 | 长安大学 | A kind of method of gear pair geometrical contact analysis |
Non-Patent Citations (2)
| Title |
|---|
| Ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法;蒋进科;方宗德;刘钊;;西安交通大学学报(06);全文 * |
| 基于Ease-off的螺旋锥齿轮齿面分区修形方法;严宏志;肖蒙;胡志安;艾伍轶;明兴祖;;中南大学学报(自然科学版)(04);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110826158A (en) | 2020-02-21 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110826158B (en) | Spiral bevel gear tooth surface Ease-off modification design method based on minimum meshing impact | |
| CN110929349B (en) | Ease-off spiral bevel gear tooth surface free shaping method | |
| CN110968918B (en) | Free-modification helical gear bearing contact analysis method considering basic joint error | |
| CN109241683B (en) | Design method for free tooth surface of helical gear | |
| US20140256223A1 (en) | Machining Method for Hard-Fine Machining of Noise-Optimized Gears on a Gear-Cutting Machine | |
| Feng et al. | Geometric design and analysis of face-gear drive with involute helical pinion | |
| CN105156637B (en) | A kind of oblique line flank of tooth gear driving pair and facewidth geometric design method | |
| CN110263367B (en) | Three-dimensional tooth profile design method of harmonic reducer without interference meshing | |
| CN107944174B (en) | Method for obtaining tooth direction load distribution coefficient of cylindrical gear | |
| CN108730480B (en) | Cycloidal gear of RV reducer and tooth profile reverse active modification method thereof | |
| CN109214093B (en) | Method for repairing concave-tip point design defect of pitch curve of N-blade non-circular gear | |
| CN105223814A (en) | Involute gear formed grinding wheel computing method | |
| Guan et al. | Comparative analysis of three geometric models for crown gear coupling | |
| CN113486466B (en) | Linear contact spiral bevel gear shaping method | |
| CN108331899A (en) | A kind of RV retarders cycloid gear profile modification design method and system | |
| CN117634057B (en) | Spiral bevel gear time-varying meshing stiffness calculation method containing peeling fault | |
| CN108345272A (en) | Gear shaping process determination method and device, terminal and industrial robot | |
| CN109376456A (en) | Contact force contact performance numerical computation method of the spiral bevel gear containing installation error | |
| CN108470102B (en) | Small wheel tooth surface design method and machining method for meshing performance pre-control | |
| CN111259499A (en) | Conical surface gear pair and design method | |
| CN109977579B (en) | Machine tool machining parameter optimization method for improving hypoid gear meshing quality | |
| CN102581384A (en) | Gear shaping method based on equal cutting area | |
| CN111539084A (en) | Involute tooth profile non-circular gear pair three-dimensional solid modeling method | |
| CN115169196A (en) | High-bearing cylindrical gear design method based on curve type meshing line | |
| CN115270347A (en) | Involute gear tooth surface modification design method considering contact ratio |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |